Identifying polymer states by machine learning

Machine learning for structure-property mapping of Ising models: Scalability and limitations

We present a scalable machine learning (ML) framework for predicting intensive properties and particularly classifying phases of Ising models. Scalability and transferability are central to the unprecedented computational efficiency of ML methods. In general, linear-scaling computation can be achieved through the divide-and-conquer approach, and the locality of physical properties is key to partitioning the system into subdomains that can be solved separately. Based on the locality assumption, ML model is developed for the prediction of intensive properties of a finite-size block. Predictions of large-scale systems can then be obtained by averaging results of the ML model from randomly sampled blocks of the system. We show that the applicability of this approach depends on whether the block-size of the ML model is greater than the characteristic length scale of the system. In particular, in the case of phase identification across a critical point, the accuracy of the ML prediction is limited by the diverging correlation length. We obtain an intriguing scaling relation between the prediction accuracy and the ratio of ML block size over the spin-spin correlation length. Implications for practical applications are also discussed. While the two-dimensional Ising model is used to demonstrate the proposed approach, the ML framework can be generalized to other many-body or condensed-matter systems.

Integrating Machine Learning in the Coarse-Grained Molecular Simulation of Polymers

Machine learning (ML) is having an increasing impact on the physical sciences, engineering, and technology and its integration into molecular simulation frameworks holds great potential to expand their scope of applicability to complex materials and facilitate fundamental knowledge and reliable property predictions, contributing to the development of efficient materials design routes. The application of ML in materials informatics in general, and polymer informatics in particular, has led to interesting results, however great untapped potential lies in the integration of ML techniques into the multiscale molecular simulation methods for the study of macromolecular systems, specifically in the context of Coarse Grained (CG) simulations. In this Perspective, we aim at presenting the pioneering recent research efforts in this direction and discussing how these new ML-based techniques can contribute to critical aspects of the development of multiscale molecular simulation methods for bulk complex chemical systems, especially polymers. Prerequisites for the implementation of such ML-integrated methods and open challenges that need to be met toward the development of general systematic ML-based coarse graining schemes for polymers are discussed.

The Effect of Machine Learning Algorithms on the Prediction of Layer-by-Layer Coating Properties

Layer-by-layer film (LbL) coatings made of polyelectrolytes are a powerful tool for surface modification, including the applications in the biomedical field, for food packaging, and in many electrochemical systems. However, despite the number of publications related to LbL assembly, predicting LbL coating properties represents quite a challenge, can take a long time, and be very costly. Machine learning (ML) methodologies that are now emerging can accelerate and improve new coating development and potentially revolutionize the field. Recently, we have demonstrated a preliminary ML-based model for coating thickness prediction. In this paper, we compared several ML algorithms for optimizing a methodology for coating thickness prediction, namely, linear regression, Support Vector Regressor, Random Forest Regressor, and Extra Tree Regressor. The current research has shown that learning algorithms are effective in predicting the coating output value, with the Extra Tree Regressor algorithm demonstrating superior predictive performance, when used in combination with optimized hyperparameters and with missing data imputation. The best predictors of the coating thickness were determined, and they can be later used to accurately predict coating thickness, avoiding measurement of multiple parameters. The development of optimized methodologies will ensure different reliable predictive models for coating property/function relations. As a continuation, the methodology can be adapted and used for predicting the outputs connected to antimicrobial, anti-inflammatory, and antiviral properties in order to be able to respond to actual biomedical problems such as antibiotic resistance, implant rejection, or COVID-19 outbreak.

Unraveling the morphological complexity of two-dimensional macromolecules

2D macromolecules, such as graphene and graphene oxide, possess a rich spectrum of conformational phases. However, their morphological classification has only been discussed by visual inspection, where the physics of deformation and surface contact cannot be resolved. We employ machine learning methods to address this problem by exploring samples generated by molecular simulations. Features such as metric changes, curvature, conformational anisotropy and surface contact are extracted. Unsupervised learning classifies the morphologies into the quasi-flat, folded, crumpled phases and interphases using geometrical and topological labels or the principal features of the 2D energy map. The results are fed into subsequent supervised learning for phase characterization. The performance of data-driven models is improved notably by integrating the physics of geometrical deformation and topological contact. The classification and feature extraction characterize the microstructures of their condensed phases and the molecular processes of adsorption and transport, comprehending the processing-microstructures-performance relation in applications.

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Morphology of 2D macromolecules are classified into four phases

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Data-driven models capture physics and topology beyond the geometry

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Condensed-phase properties are understood by the features extracted

Resolving morphological complexity of macromolecules is the stepping stone to the design and fabrication of high-performance, multi-functional materials and to understanding the soft matter behaviors in biology and engineering. To extract the physics of lattice distortion and surface contact beyond the conformation is critical, yet challenging. Here, we show that, by labeling the simulation data using the 2D map of potential energies, the 3D geometry, and the topology of contact, morphological classification can be achieved with high accuracy. The well-trained model can be used to decipher the microstructural complexity using simulation or experimental data, which may include the geometrical representation only. This data-driven approach extracts the key geometrical and topological features of 2D macromolecules that are directly responsible for the material performance in relevant applications and can be extended to study other complex surfaces such as red blood cells and the brain.

Machine learning approaches for biomolecular, biophysical, and biomaterials research

A fluent conversation with a virtual assistant, person-tailored news feeds, and deep-fake images created within seconds-all those things that have been unthinkable for a long time are now a part of our everyday lives. What these examples have in common is that they are realized by different means of machine learning (ML), a technology that has fundamentally changed many aspects of the modern world. The possibility to process enormous amount of data in multi-hierarchical, digital constructs has paved the way not only for creating intelligent systems but also for obtaining surprising new insight into many scientific problems. However, in the different areas of biosciences, which typically rely heavily on the collection of time-consuming experimental data, applying ML methods is a bit more challenging: Here, difficulties can arise from small datasets and the inherent, broad variability, and complexity associated with studying biological objects and phenomena. In this Review, we give an overview of commonly used ML algorithms (which are often referred to as "machines") and learning strategies as well as their applications in different bio-disciplines such as molecular biology, drug development, biophysics, and biomaterials science. We highlight how selected research questions from those fields were successfully translated into machine readable formats, discuss typical problems that can arise in this context, and provide an overview of how to resolve those encountered difficulties.

Forming a Double-Helix Phase of Single Polymer Chains by the Cooperation between Local Structure and Nonlocal Attraction

Double-helix structures, such as DNA, are formed in nature to realize many unique functions. Inspired by this, researchers are pursuing strategies to design such structures from polymers. A key question is whether the double helix can be formed from the self-folding of a single polymer chain without specific interactions. Here, using Langevin dynamics simulation and theoretical analysis, we find that a stable double-helix phase can be achieved by the self-folding of single semiflexible polymers as a result of the cooperation between local structure and nonlocal attraction. The critical temperature of double-helix formation approximately follows T^{cri}∼ln(k_{θ}) and T^{cri}∼ln(k_{τ}), where k_{θ} and k_{τ} are the polymer bending and torsion stiffness, respectively. Furthermore, the double helix can exhibit major and minor grooves due to symmetric break for better packing. Our results provide a novel guide to the experimental design of the double helix.

Supervised and unsupervised machine learning of structural phases of polymers adsorbed to nanowires

We identify configurational phases and structural transitions in a polymer nanotube composite by means of machine learning. We employ various unsupervised dimensionality reduction methods, conventional neural networks, as well as the confusion method, an unsupervised neural-network-based approach. We find neural networks are able to reliably recognize all configurational phases that have been found previously in experiment and simulation. Furthermore, we locate the boundaries between configurational phases in a way that removes human intuition or bias. This could be done before only by relying on preconceived, ad hoc order parameters.

Integration of Machine Learning and Coarse-Grained Molecular Simulations for Polymer Materials: Physical Understandings and Molecular Design

In recent years, the synthesis of monomer sequence-defined polymers has expanded into broad-spectrum applications in biomedical, chemical, and materials science fields. Pursuing the characterization and inverse design of these polymer systems requires our fundamental understanding not only at the individual monomer level, but also considering the chain scales, such as polymer configuration, self-assembly, and phase separation. However, our accessibility to this field is still rudimentary due to the limitations of traditional design approaches, the complexity of chemical space along with the burdened cost and time issues that prevent us from unveiling the underlying monomer sequence-structure-property relationships. Fortunately, thanks to the recent advancements in molecular dynamics simulations and machine learning (ML) algorithms, the bottlenecks in the tasks of establishing the structure-function correlation of the polymer chains can be overcome. In this review, we will discuss the applications of the integration between ML techniques and coarse-grained molecular dynamics (CGMD) simulations to solve the current issues in polymer science at the chain level. In particular, we focus on the case studies in three important topics—polymeric configuration characterization, feed-forward property prediction, and inverse design—in which CGMD simulations are leveraged to generate training datasets to develop ML-based surrogate models for specific polymer systems and designs. By doing so, this computational hybridization allows us to well establish the monomer sequence-functional behavior relationship of the polymers as well as guide us toward the best polymer chain candidates for the inverse design in undiscovered chemical space with reasonable computational cost and time. Even though there are still limitations and challenges ahead in this field, we finally conclude that this CGMD/ML integration is very promising, not only in the attempt of bridging the monomeric and macroscopic characterizations of polymer materials, but also enabling further tailored designs for sequence-specific polymers with superior properties in many practical applications.

Decoding Interaction Patterns from the Chemical Sequence of Polymers Using Neural Networks

The relation between chemical sequences and the properties of polymers is considered using artificial neural networks with a low-dimensional bottleneck layer of neurons. These encoder-decoder architectures may compress the input information into a meaningful set of physical variables that describe the correlation between distinct types of data. In this work, neural networks were trained to translate a sequence of hydrophilic and hydrophobic segments into the effective free energy landscape of a copolymer interacting with a lipid membrane. The training data were obtained by the sampling of coarse-grained polymer conformations in a given membrane density field. Neural networks that were split into separate channels have learned to decompose the free energy into independent components that are explainable by known concepts from polymer physics. The semantic information in the hidden layers was employed to predict polymer translocation events through a membrane for a more detailed dynamic model via a transfer learning procedure. The search for minimal translocation times in the compressed chemical space underlined that nontrivial sequence motifs may lead to optimal properties.

Phase classification using neural networks: application to supercooled, polymorphic core-softened mixtures

Characterization of phases of soft matter systems is a challenge faced in many physical chemical problems. For polymorphic fluids it is an even greater challenge. Specifically, glass forming fluids, as water, can have, besides solid polymorphism, more than one liquid and glassy phases, and even a liquid-liquid critical point. In this sense, we apply a neural network algorithm to analyze the phase behavior of a mixture of core-softened fluids that interact through the continuous-shouldered well (CSW) potential, which have liquid polymorphism and liquid-liquid critical points, similar to water. We also apply the neural network to mixtures of CSW fluids and core-softened alcohols models. We combine and expand methods based on bond-orientational order parameters to study mixtures, applied to mixtures of hardcore fluids and to supercooled water, to include longer range coordination shells. With this, the trained neural network was able to properly predict the crystalline solid phases, the fluid phases and the amorphous phase for the pure CSW and CSW-alcohols mixtures with high efficiency. More than this, information about the phase populations, obtained from the network approach, can help verify if the phase transition is continuous or discontinuous, and also to interpret how the metastable amorphous region spreads along the stable high density fluid phase. These findings help to understand the behavior of supercooled polymorphic fluids and extend the comprehension of how amphiphilic solutes affect the phases behavior.

Characterising soft matter using machine learning

Machine learning is making a major impact in materials research. I review current progress across a selection of areas of ubiquitous soft matter. When applied to particle tracking, machine learning using convolution neural networks is providing impressive performance but there remain some significant problems to solve. Characterising ordered arrangements of particles is a huge challenge and machine learning has been deployed to create the description, perform the classification and tease out an interpretation using a wide array of techniques often with good success. In glass research, machine learning has proved decisive in quantifying very subtle correlations between the local structure around a site and the susceptibility towards a rearrangement event at that site. There are also beginning to be some impressive attempts to deploy machine learning in the design of composite soft materials. The discovery aspect of this new materials design meets the current interest in teaching algorithms to learn to extrapolate beyond the training data.

Automation and data-driven design of polymer therapeutics

Polymers are uniquely suited for drug delivery and biomaterial applications due to tunable structural parameters such as length, composition, architecture, and valency. To facilitate designs, researchers may explore combinatorial libraries in a high throughput fashion to correlate structure to function. However, traditional polymerization reactions including controlled living radical polymerization (CLRP) and ring-opening polymerization (ROP) require inert reaction conditions and extensive expertise to implement. With the advent of air-tolerance and automation, several polymerization techniques are now compatible with well plates and can be carried out at the benchtop, making high throughput synthesis and high throughput screening (HTS) possible. To avoid HTS pitfalls often described as "fishing expeditions," it is crucial to employ intelligent and big data approaches to maximize experimental efficiency. This is where the disruptive technologies of machine learning (ML) and artificial intelligence (AI) will likely play a role. In fact, ML and AI are already impacting small molecule drug discovery and showing signs of emerging in drug delivery. In this review, we present state-of-the-art research in drug delivery, gene delivery, antimicrobial polymers, and bioactive polymers alongside data-driven developments in drug design and organic synthesis. From this insight, important lessons are revealed for the polymer therapeutics community including the value of a closed loop design-build-test-learn workflow. This is an exciting time as researchers will gain the ability to fully explore the polymer structural landscape and establish quantitative structure-property relationships (QSPRs) with biological significance.

Identifying knot types of polymer conformations by machine learning

We investigate the use of artificial neural networks (NNs) as an alternative tool to current analytical methods for recognizing knots in a given polymer conformation. The motivation is twofold. First, it is of interest to examine whether NNs are effective at learning the global and sequential properties that uniquely define a knot. Second, knot classification is an important and unsolved problem in mathematical and physical sciences, and NNs may provide insights into this problem. Motivated by these points, we generate millions of polymer conformations for five knot types: 0, 3_{1}, 4_{1}, 5_{1}, and 5_{2}, and we design various NN models for classification. Our best model achieves a five-class classification accuracy of above 99% on a polymer of 100 monomers. We find that the sequential modeling ability of recurrent NNs is crucial for this result, as it outperforms feed-forward NNs and successfully generalizes to differently sized conformations as well. We present our methods and suggest that deep learning may be used in specific applications of knot detection where some error is permissible. Hopefully, with further development, NNs can offer an alternative computational method for knot identification and facilitate knot research in mathematical and physical sciences.

Structural Prediction and Inverse Design by a Strongly Correlated Neural Network

Macromolecules contain molecular units as the coding information for their correlated structures in physical dimensions. The relationship between these two features is governed by the interaction energies of the involved molecular units and their encoded sequences. We present a neural network algorithm that treats molecular units themselves as neural networks, which has the flexibility to allow each unit to respond to its own environment and to influence others in the system. Through a deep neural network and a self-consistent procedure, molecular units in the network establish a strong correlation to produce the desirable features in the physical world. The proposed framework is applied to the HP model. Both the forward problem of predicting folded structures from given sequences and the inverse problem of predicting required sequences for a given structure are examined.

Generating the conformational properties of a polymer by the restricted Boltzmann machine

In polymer theory, computer-generated polymer configurations, by either Monte Carlo simulations or molecular dynamics simulations, help us to establish the fundamental understanding of the conformational properties of polymers. Here, we introduce a different method, exploiting the properties of a machine-learning algorithm, the restricted Boltzmann machine network, to generate independent polymer configurations for self-avoiding walks (SAWs), for studying the conformational properties of polymers. We show that with adequate training data and network size, this method can capture the underlying polymer physics simply from learning the statistics in the training data without explicit information on the physical model itself. We critically examine how the trained Boltzmann machine can generate independent configurations that are not in the original training data set of SAWs.

Machine learning topological defects of confined liquid crystals in two dimensions

Supervised machine learning can be used to classify images with spatially correlated physical features. We demonstrate the concept by using the coordinate files generated from an off-lattice computer simulation of rodlike molecules confined in a square box as an example. Because of the geometric frustrations at high number density, the nematic director field develops an inhomogeneous pattern containing various topological defects as the main physical feature. We describe two machine-learning procedures that can be used to effectively capture the correlation between the defect positions and the nematic directors around them and hence classify the topological defects. First is a feedforward neural network, which requires the aid of presorting the off-lattice simulation data in a coarse-grained fashion. Second is a recurrent neural network, which needs no such sorting and can be directly used for finding spatial correlations. The issues of when to presort a simulation data file and how the network structures affect such a decision are addressed.

A high-bias, low-variance introduction to Machine Learning for physicists

Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, generalization, and gradient descent before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python Jupyter notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists may be able to contribute.

Recognition of polymer configurations by unsupervised learning

Unsupervised learning as an important branch of machine learning is commonly adopted to discover patterns, with the purpose of conducting data clustering without being labeled in advance. In this study, we elucidate the striking ability of unsupervised learning techniques in exploring the phase transitions of polymer configurations. In order to extract the low-dimensional representation of polymer configurations, principal component analysis and diffusion map are applied to distinguish the coiled state and collapsed states and further detect the delicate distinction among collapsed states, respectively. These dimensionality reduction techniques not only identify the distinct states in the feature space, but also offer significant insights to understand the relation between salient features and order parameters in physics. In addition, a hybrid neural network scheme combining the supervised learning and unsupervised learning is utilized to precisely detect the critical point of phase transition between polymer configurations. Our study demonstrates a promising strategy based on the unsupervised learning, particularly in the exploration of phase transition in polymeric systems.

Machine Learning Models for Predicting and Classifying the Tensile Strength of Polymeric Films Fabricated via Different Production Processes

In this study, machine learning algorithms (MLA) were employed to predict and classify the tensile strength of polymeric films of different compositions as a function of processing conditions. Two film production techniques were investigated, namely compression molding and extrusion-blow molding. Multi-factor experiments were designed with corresponding parameters. A tensile test was conducted on samples and the tensile strength was recorded. Predictive and classification models from nine MLA were developed. Performance analysis demonstrated the superior predictive ability of the support vector machine (SVM) algorithm, in which a coefficient of determination and mean absolute percentage error of 96% and 4%, respectively were obtained for the extrusion-blow molded films. The classification performance of the MLA was also evaluated, with several algorithms exhibiting excellent performance.

Confusion scheme in machine learning detects double phase transitions and quasi-long-range order

Thanks to the development of machine learning techniques, it has been shown that the supervised learning can be useful to study critical phenomena of various systems. However, the supervised learning cannot be done without labels which require knowledge about critical behavior of the system. To overcome this barrier, unsupervised machine learning methods have been considered and the confusion scheme has been proposed. In this study, we use the confusion scheme of the unsupervised learning and investigate critical behavior of various systems which exhibit single (double) phase transitions with (without) quasi-long-range order. In detail, we choose the two-color Ashkin-Teller model, the XY model, and the eight-state clock model as such systems and snapshots of the spin configurations at various temperatures are collected via Monte Carlo simulations to be used as input data for the unsupervised machine learning. We also put focus on the size dependence of results and validate the availability of the confusion scheme in thermodynamic limit. Our results indicate that the confusion scheme of the unsupervised learning successfully locates the approximate transition points for all models and becomes more accurate as the system size is increased. We also find a characteristic feature of the result which reflects the presence of a quasi-long-range order. We conclude that regardless of the presence of a quasi-long-range order, single and double phase transitions can be detected via the confusion scheme.

Estimating physical properties from liquid crystal textures via machine learning and complexity-entropy methods

Imaging techniques are essential tools for inquiring a number of properties from different materials. Liquid crystals are often investigated via optical and image processing methods. In spite of that, considerably less attention has been paid to the problem of extracting physical properties of liquid crystals directly from textures images of these materials. Here we present an approach that combines two physics-inspired image quantifiers (permutation entropy and statistical complexity) with machine learning techniques for extracting physical properties of nematic and cholesteric liquid crystals directly from their textures images. We demonstrate the usefulness and accuracy of our approach in a series of applications involving simulated and experimental textures, in which physical properties of these materials (namely: average order parameter, sample temperature, and cholesteric pitch length) are predicted with significant precision. Finally, we believe our approach can be useful in more complex liquid crystal experiments as well as for probing physical properties of other materials that are investigated via imaging techniques.

Machine Learning Based Localization and Classification with Atomic Magnetometers

We demonstrate identification of position, material, orientation, and shape of objects imaged by a ^{85}Rb atomic magnetometer performing electromagnetic induction imaging supported by machine learning. Machine learning maximizes the information extracted from the images created by the magnetometer, demonstrating the use of hidden data. Localization 2.6 times better than the spatial resolution of the imaging system and successful classification up to 97% are obtained. This circumvents the need of solving the inverse problem and demonstrates the extension of machine learning to diffusive systems, such as low-frequency electrodynamics in media. Automated collection of task-relevant information from quantum-based electromagnetic imaging will have a relevant impact from biomedicine to security.

Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination

We apply unsupervised machine learning techniques, mainly principal component analysis (PCA), to compare and contrast the phase behavior and phase transitions in several classical spin models-the square- and triangular-lattice Ising models, the Blume-Capel model, a highly degenerate biquadratic-exchange spin-1 Ising (BSI) model, and the two-dimensional XY model-and we examine critically what machine learning is teaching us. We find that quantified principal components from PCA not only allow the exploration of different phases and symmetry-breaking, but they can distinguish phase-transition types and locate critical points. We show that the corresponding weight vectors have a clear physical interpretation, which is particularly interesting in the frustrated models such as the triangular antiferromagnet, where they can point to incipient orders. Unlike the other well-studied models, the properties of the BSI model are less well known. Using both PCA and conventional Monte Carlo analysis, we demonstrate that the BSI model shows an absence of phase transition and macroscopic ground-state degeneracy. The failure to capture the "charge" correlations (vorticity) in the BSI model (XY model) from raw spin configurations points to some of the limitations of PCA. Finally, we employ a nonlinear unsupervised machine learning procedure, the "autoencoder method," and we demonstrate that it too can be trained to capture phase transitions and critical points.